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##### Q-27. Calculation follows: $ P_{\text{up}} = \frac{e^{r\Delta t} - d}{u - d} = \frac{e^{0.12 \times 3/12} - 0.8}{1.2 - 0.8} = 57.61\% $ | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

The calculation shows the risk-neutral probability of an up move in a binomial tree model. Given:

r = 12% annual interest rate
Δt = 3/12 = 0.25 years
u = 1.2 (up factor)
d = 0.8 (down factor)

The formula for risk-neutral probability is: $P_{\text{up}} = \frac{e^{r\Delta t} - d}{u - d}$

Substituting the values: $P_{\text{up}} = \frac{e^{0.12 \times 0.25} - 0.8}{1.2 - 0.8} = \frac{e^{0.03} - 0.8}{0.4} = \frac{1.03045 - 0.8}{0.4} = \frac{0.23045}{0.4} = 0.576125 \approx 57.61\%$

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Q-27.

Calculation follows: $P_{\text{up}} = \frac{e^{r\Delta t} - d}{u - d} = \frac{e^{0.12 \times 3/12} - 0.8}{1.2 - 0.8} = 57.61\%$

Q-27.

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Financial Risk Manager Part 1

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Get started today

Q-27. Calculation follows: Pup=erΔt−du−d=e0.12×3/12−0.81.2−0.8=57.61%P_{\text{up}} = \frac{e^{r\Delta t} - d}{u - d} = \frac{e^{0.12 \times 3/12} - 0.8}{1.2 - 0.8} = 57.61\%Pup​=u−derΔt−d​=1.2−0.8e0.12×3/12−0.8​=57.61%

Q-27.

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Q-27.

Calculation follows: $P_{\text{up}} = \frac{e^{r\Delta t} - d}{u - d} = \frac{e^{0.12 \times 3/12} - 0.8}{1.2 - 0.8} = 57.61\%$